What is the limit as x approaches 2 of (|x|)/x ?

The limit as x approaches 2 of (|x|)/x is 1

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limit as x approaches 2 of (|x|)/x

x \to 2 lim (\frac{∣ x ∣}{x})

1

Solution steps

x \to 2 lim (\frac{∣ x ∣}{x})

Plug in the value

x = 2

= \frac{∣ 2 ∣}{2}

Simplify

\frac{∣ 2 ∣}{2} : 1

= 1

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x \to 0 lim (\frac{ln ∣ x ∣}{x})

θ \to - \frac{π}{2} lim (sec (θ))

What is the limit as x approaches 2 of (|x|)/x ?
The limit as x approaches 2 of (|x|)/x is 1